(ii) If \(\tilde{f}\)  takes the value \(-\infty \)  at one or more points, then the arguments in the proof of [1]} carry over and we again conclude that (REF ) holds. (iii) The case \(\tilde{f}\)  being identical to \(\infty \)  is ruled out by the assumption \(\operatorname{dom}\varphi \ne \emptyset \) . Regardless, (REF ) implies that the necessary optimality condition in Theorem REF  holds.
